As regards appearance, how about making it entirely black with a hard edge, like the edge of the map is currently? So the end appearance is that of a non-rectangular map.

There would however be subtle UI differences between off-the-map and Unaccessible terrain -- it would get an overlay as if "show native tiles" was enabled, for instance. That can't be solved without code changes. Without that, perhaps it's best if it looks distinct from off-the-map.

(Also, it occurs to me that "Inaccessible" would be a more idiomatic English name.)

Add "Unaccessible" terrain to classic, multiplayer, experimental, civ2civ3, and alien rulesets. I don't see how including these to civ1/civ2 rulesets would hurt the compatibility, but left them out anyway.
Note that alien ruleset has "Tile_Workable" effects defined so that new terrain would get the effect only if explicitly added - so no changes to alien/effects.ruleset.

Add "Unaccessible" terrain type to supplied rulesets for scenario map authors to use. It will never appear in normal generated maps. No unit can enter the tile, nor can cities work it. One can use it to "shape" map (accessible area).

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